What is meant by “tape” 1, depicted in FIG. 1, is a segment of composite material comprising fibres, or of woven material, of elongate shape extending in a longitudinal direction dLong with a thin cross section Sec that is symmetric with respect to the longitudinal direction dLong, the thickness of the cross section Sec typically being negligible by comparison with the width and length of the tape 1.
In this particular instance, the tape 1 extends in the longitudinal direction dLong and has a plane of symmetry Psym in the said longitudinal direction dLong. It comprises a composite material of which the matrix comprises a resin in which fibres extend.
A document of the prior art, EP0891248, proposes an extendable element that can be configured into a coiled first state in which the element is coiled substantially parallel to a first axis, and into an extended second state in which the element extends substantially parallel to a second axis. The extendable element is made up of a substrate and of at least one fibrous layer of which the fibres are crossed. Each of the fibres is oriented at an angle of between 0 degrees and 90 degrees with respect to the first axis such that when the element is extended in a direction substantially parallel to the second axis, said crossed fibres cause contraction in a direction oriented at a certain angle to the second axis, so as to place the element in the second state.
Let it be noted that all the angular offsets mentioned in the remainder of this application are oriented in the clockwise or negative trigonometric direction.
Moreover, it is also known practice to create tapes 1 by superposing layers comprising a first fibrous material, according to the principle depicted in FIGS. 2a and 2b. 
More specifically, FIG. 2a relates to a tape comprising a stack Emp or superposition of four fibrous layers. The direction of orientation of the fibres of one of the layers Cn form an angular offset α with respect to the longitudinal direction dLong, the angular offset α being between 0° and 90°. The fibres of the other layer Cn+1 make an angular offset (π−α) with the longitudinal direction dLong. In other words, the entirety of one layer comprises at least one first group of fibres of which the direction makes a first angular offset α with the longitudinal direction dLong and the entirety of the next layer comprises the first group of fibres of which the direction forms an angular offset (π−α) with respect to the longitudinal direction dLong.
FIG. 2b is a depiction of the stack Emp of FIG. 2a; it is made up of four fibrous layers Cn of which the direction of the fibres forms an angular offset with respect to the longitudinal direction dLong, the value of the angular offset alternating between (+α) and (π−α) between the layer Cn and the next layer Cn+1.
This type of antisymmetric tape avoids coupling between bending and torsion but on the other hand is sensitive to temperature variations, as FIGS. 3a and 3b demonstrate.
FIG. 3a schematically depicts a tape 1 comprising two layers of fibrous composite materials of which the fibres of the first layer C1 are oriented in a first direction d1 and the fibres of the second layer C2 are oriented in a second direction d2. Under the effect of an increase in temperature in particular, the layers of composite material C1, C2 each expand in a direction transverse to the direction of the fibres, since the fibres have a very low expansion coefficient, of the order of a few 10−6K−1, such that twisting of the tape 1 is observed.
FIG. 3b clearly shows the torsion that arises when the tape 1 is subjected to variations in temperature. Specifically, the tape 1 (on the left) which extends in the longitudinal direction dLong has a cross section Sec of which the value of the radius of curvature rs in a transverse direction dTransv perpendicular to the longitudinal direction dLong is substantially constant over the entire cross section Sec; in other words, the tape 1 has a shape that is uniformly substantially concave. Following an increase in temperature, a greater turning-up of two of the diagonally opposite vertices of the tape 1 may be observed, notably in the right-hand figure.
It will therefore be readily appreciated that a tape 1 that twists in the event of variations in temperature will not be able to be wound and/or unwound cylindrically.
FIGS. 4a-4d depict a process for the deployment of a conventional tape as it passes from a fully wound state in FIG. 4a to a fully unwound state in FIG. 4d, the unwinding process being said to be chaotic. FIGS. 4b and 4c illustrate intermediate states exhibiting several wound zones and/or several unwound zones. The unwinding process is jerky and uneven.
Contrary to the chaotic unwinding process, a process for the unwinding of a tape 1 between a wound first state and an unwound second state is qualified as “smooth” when all of the intermediate states between the first and the second state comprise a single continuous portion of wound tape of which the value of the radius of curvature is higher than a threshold value and a single continuous portion of unwound tape of which the value of the radius of curvature is less than the threshold value and is continuous over the unwound portion. In other words, the unwinding process occurs uniformly with no zone in which the tape 1 is kinked. During the unwinding process, the length of the continuous wound portion of tape decreases over time and that of the continuous unwound portion increases over time.